1. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Fundamental Theorem of Calculus Section 5.4

2. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 2 What you’ll learn about Fundamental Theorem, Part 1 Graphing the Function Fundamental Theorem, Part 2 Area Connection Analyzing Antiderivatives Graphically … and why The Fundamental Theorem of Calculus is a Triumph of Mathematical Discovery and the key to solving many problems.

3. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 3 The Fundamental Theorem of Calculus

4. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 4 The Fundamental Theorem of Calculus

5. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 5 Example Applying the Fundamental Theorem

6. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 6 Example The Fundamental Theorem with the Chain Rule

7. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 7 Example Variable Lower Limits of Integration

8. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 8 The Fundamental Theorem of Calculus, Part 2

9. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 9 The Fundamental Theorem of Calculus, Part 2

10. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 10 Example Evaluating an Integral

11. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 11 How to Find Total Area Analytically

12. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 12 How to Find Total Area Numerically

13. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Page 286 (1-29 odd) ========================= Page 287 (35-45 odd) Slide 5- 13